Multiplication rule for "AND"

Lessons

• Introduction
  P(A and B) VS. P(A or B)
  
  P(A and B): probability of event A occurring and then event B occurring in successive trials.
  P(A or B):

  probability of event A occurring or event B occurring during a single trial.

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• 1.
  Multiplication Rule for “AND”
  A coin is tossed, and then a die is rolled.
  What is the probability that the coin shows a head and the die shows a 4?

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• 2.
  Independent Events VS. Dependent Events
  a)

  One card is drawn from a standard deck of 52 cards and is not replaced. A second card is then drawn.
  Consider the following events:
  A = {the $1^{st}$ card is an ace}
  B = {the $2^{nd}$ card is an ace}
  Determine:
  $\cdot$ P(A)
  $\cdot$ P(B)
  $\cdot$ Are events A, B dependent or independent?
  $\cdot$ P(A and B), using both the tree diagram and formula
  
  
  b)

  One card is drawn from a standard deck of 52 cards and is replaced. A second card is then drawn.
  Consider the following events:
  A = {the $1^{st}$ card is an ace}
  B = {the $2^{nd}$ card is an ace}
  Determine:
  $\cdot$ P(A)
  $\cdot$ P(B)
  $\cdot$ Are events A, B dependent or independent?
  $\cdot$ P(A and B), using both the tree diagram and formula
  
  

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• 3.
  Bag A contains 2 red balls and 3 green balls. Bag B contains 1 red ball and 4 green balls.
  A fair die is rolled: if a 1 or 2 comes up, a ball is randomly selected from Bag A;
  

  if a 3, 4, 5, or 6 comes up, a ball is randomly selected from Bag B.
  
  a)

  What is the probability of selecting a green ball from Bag A?
  
  
  b)

  What is the probability of selecting a green ball?
  
  

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